Statistical dispersion

In statistics, dispersion (also called variability, scatter, or spread) is the extent to which a distribution is stretched or squeezed.

[1] Common examples of measures of statistical dispersion are the variance, standard deviation, and interquartile range.

Dispersion is contrasted with location or central tendency, and together they are the most used properties of distributions.

Robust measures of scale are those unaffected by a small number of outliers, and include the IQR and MAD.

All the above measures of statistical dispersion have the useful property that they are location-invariant and linear in scale.

The Allan variance can be used for applications where the noise disrupts convergence.

[2] The Hadamard variance can be used to counteract linear frequency drift sensitivity.

[3] For categorical variables, it is less common to measure dispersion by a single number; see qualitative variation.

The standard deviation is an important measure in fluctuation theory, which explains many physical phenomena, including why the sky is blue.

[4] In the biological sciences, the quantity being measured is seldom unchanging and stable, and the variation observed might additionally be intrinsic to the phenomenon: It may be due to inter-individual variability, that is, distinct members of a population differing from each other.

Such types of variability are also seen in the arena of manufactured products; even there, the meticulous scientist finds variation.